{
  "id": "1310.3075",
  "version": "v1",
  "published": "2013-10-11T10:21:58.000Z",
  "updated": "2013-10-11T10:21:58.000Z",
  "title": "Product formulas for a two-parameter family of Heckman-Opdam hypergeometric functions of type BC",
  "authors": [
    "Michael Voit"
  ],
  "categories": [
    "math.CA",
    "math.RT"
  ],
  "abstract": "In this paper we present explicit product formulas for a continuous two-parameter family of Heckman-Opdam hypergeometric functions of type BC on Weyl chambers $C_q\\subset \\mathbb R^q$ of type $B$. These formulas are related to continuous one-parameter families of probability-preserving convolution structures on $C_q\\times\\mathbb R$. These convolutions on $C_q\\times\\mathbb R$ are constructed via product formulas for the spherical functions of the symmetric spaces $U(p,q)/ (U(p)\\times SU(q))$ and associated double coset convolutions on $C_q\\times\\mathbb T$ with the torus $\\mathbb T$. We shall obtain positive product formulas for a restricted parameter set only, while the associated convolutions are always norm-decreasing. Our paper is related to recent positive product formulas of R\\\"osler for three series of Heckman-Opdam hypergeometric functions of type BC as well as to classical product formulas for Jacobi functions of Koornwinder and Trimeche for rank $q=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-11T10:21:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C67",
      "43A90",
      "43A62",
      "33C80"
    ],
    "keywords": [
      "heckman-opdam hypergeometric functions",
      "type bc",
      "two-parameter family",
      "positive product formulas",
      "explicit product formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.3075V"
    }
  }
}